14 23 27 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 23   c = 27

Area: T = 160.997689438
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 31.232225881° = 31°13'56″ = 0.54551057491 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 90.35658766952° = 90°21'21″ = 1.57770075469 rad

Height: ha = 232.99955634
Height: hb = 143.9997299461
Height: hc = 11.926569588

Median: ma = 24.08331891576
Median: mb = 18.17327818454
Median: mc = 13.42657215821

Inradius: r = 5.03111529494
Circumradius: R = 13.55002604142

Vertex coordinates: A[27; 0] B[0; 0] C[7.33333333333; 11.926569588]
Centroid: CG[11.44444444444; 3.975523196]
Coordinates of the circumscribed circle: U[13.5; -0.08438525492]
Coordinates of the inscribed circle: I[9; 5.03111529494]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.768774119° = 148°46'4″ = 0.54551057491 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 89.64441233048° = 89°38'39″ = 1.57770075469 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 14 ; ; b = 23 ; ; c = 27 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 14+23+27 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-14)(32-23)(32-27) } ; ; T = sqrt{ 25920 } = 161 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 161 }{ 14 } = 23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 161 }{ 23 } = 14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 161 }{ 27 } = 11.93 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 14**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 31° 13'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-14**2-27**2 }{ 2 * 14 * 27 } ) = 58° 24'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-14**2-23**2 }{ 2 * 23 * 14 } ) = 90° 21'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 161 }{ 32 } = 5.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 13'56" } = 13.5 ; ;




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